On the calculation of predeformation-dependent dynamic modulus tensors in finite nonlinear viscoelasticity
On the calculation of predeformation-dependent dynamic modulus tensors in finite nonlinear viscoelasticity
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DOI：
10.1016/j.mechrescom.2009.02.005
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发表时间：
2009-09
影响因子：
2.4
通讯作者：
A. Lion;J. Retka;M. Rendek
中科院分区：
文献类型：
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作者：
A. Lion;J. Retka;M. Rendek
为了模拟非线性粘弹性结构在有限预变形和小振幅叠加简谐变形共同作用下的频率相关行为，需要建立本构模型的频域公式。为此，考虑了最近发展起来的一种有限粘弹性方法，并导出了相应的动弹模张量。在预变形附近对本构方程进行几何线性化，并在频域中进行计算。此程序适用于任意本构模型，并可用于推导它们的频域公式，用于有限元实现，如Morman和Nagtegaal[Morman，K.N.，Nagtegaal，J.C.，1983]。变形粘弹性固体中正弦小振幅振动的有限元分析。国际工程数值方法杂志，19,1079-1103]。
To simulate the frequency-dependent behaviour of nonlinear viscoelastic structures under loadings which consist of a finite predeformation in combination with a superimposed harmonic deformation with small amplitude, frequency-domain formulations of the constitutive models are needed. For this purpose, a recently developed approach of finite viscoelasticity is considered and the corresponding dynamic modulus tensors are derived. The constitutive equations are geometrically linearized in the neighbourhood of the predeformation and evaluated in the frequency-domain. This procedure is applicable to arbitrary constitutive models and can be used to derive their frequency-domain formulations for finite element implementations as proposed by Morman and Nagtegaal [Morman, K.N., Nagtegaal, J.C., 1983. Finite element analysis of sinusoidal small-amplitude vibrations in deformed viscoelastic solids. International Journal for Numerical Methods in Engineering, 19, 1079–1103].